Ortogonalidad, Teoría de Aproximación y Aplicaciones. Print
Written by Guillermo López Lagomasino   
Sunday, 05 April 2009 00:00

 

Title; Ortogonalidad, Teoría de Aproximación y Aplicaciones.

Code: BFM2003-06335-C03-02.

Center: Ministerio de Educación y Ciencia de España.

Period: November, 2003- Novermber, 2006.

Head: G. López Lagomasino

Number of participants: 20


Summary  


The aim of this project  is to investigate the analytical properties of orthogonal polynomials with respect to different orthogonality models: (a) classical: with respect to a positive measure (on the real line, on the unit circle or, in general, on any subset of the complex plane); (b) matrix: with respect to a positive definite matrix of measures on the real line; (c) Sobolev: where the derivatives of polynomials are involved; together with other related fields such as: moment problems, q-polynomials (with applications to different discrete models of cuantic oscilators), rational approximation (Padé type approximants and their extensions, with applications to estability of retarded dynamical systems together with computational methods for special functions which are relevant in physical-mathematical models) and, in general, approximation theory. The techniques used are Matrix Analysis, Potential Theory, Fourier Analysis, Operator Theory and Interpolation, which provide a theoretical frame for the computational aspects involved in such problems.

 List of Publications  

 (you can download a copy of a given article visiting the home page of the team member)

 


 

  1. U. Fidalgo, G. López Lagomasino. General results on the convergence of multipoint Hermite-Padé approximants of Nikishin systems. Constructive Approximation, 25 (2007), 89-107.
  2. D. Barrios Rolanía, G. López Lagomasino. Asymptotic behavior of solutions of general three term recurrence relations. Advances in Computational Mathematics, 26 (2007): 9-37.
  3. U. Fidalgo, G. López Lagomasino. Rate of convergence of generalized Hermite-Padé approximants of Nikishin systems. Constructive Approximation, 23 (2006), 165-196.
  4. D. Barrios, B. de la Calle, G. López Lagomasino. Ratio and relative asymptotic of polynomials orthogonal with respect to varying Denisov-type measures. J. of Approx. Theory, 139 (2006), 223-256.
  5. A. I. Aptekarev, V. Kalyagin, G. López Lagomasino, I. A. Rocha. On the limit behavior of the recurrence coefficients for multiple orthogonal polynomials. J. of Approx. Theory, 139 (2006), 346-370.
  6. M. Bello, A. Martínez, X. Tolsa, G. López Lagomasino. Sesión monográfica de teoría de aproximación. Boletín SEMA, 34 (2006), 153-174.
  7. G. López Lagomasino, F. Marcellán, H. Pijeira. Logarithmic asymptotic of contracted Sobolev extremal polynomials on the real line. J. of Approx. Theory, 143 (2006), 62-73.
  8. A. I. Aptekarev, G. López Lagomasino, I. A. Rocha. Ratio asymptotic of Hermite-Padé polynomials for Nikishin systems. Matematicheskii Sbornik, 196 (2005), 1089-1107.
  9. G. López Lagomasino, I. Pérez, H. Pijeira. Asymptotic of extremal polynomials in the complex plane. J. of Approx. Theory, 137 (2005), 226-237.
  10. M. Alfaro, F. Marcellán, A. Peña, M. L. Rezola, On linearly related orthogonal polynomials and their functionals, J. Math. Anal. and Appl. 287 (2003) 307-319.
  11. J. Hernández, F. Marcellán, C. Rodríguez. Leverrier-Fadeev algorithm and classical orthogonal polynomials, Rev. de la Acad. Col. de Cien. Exactas, Fís. y Nat.  28 (106) (2004) 39-47.
  12. M. I. Bueno, F. Marcellán,  Darboux Transformation and Perturbation of  Linear Functionals, Linear Alg. and Appl. 384 (2004) 215-242.
  13. R. Alvarez-Nodarse, J. Arvesu, F. Marcellán. On the Krall-type polynomials, J. of Appl. Math. 5 (2004) 359-370.
  14. J. Arvesu, A. Garrido, F. Marcellán, Modification of linear functionals with Dirac masses: Class of the modified linear functional, Bol. Mat.  N.S. 11 (1) (2004) 32-51.
  15. M. Alfaro, F. Marcellán, A. Peña, M. L. Rezola. On rational transformations of linear functionals. A direct problem, J. Math. Anal. and Appl. 298 (2004) 171-183.
  16. J. Hernández, F. Marcellán. An extension of Leverrier-Faddeev algorithm using a basis of classical orthogonal polynomials,  Facta Univ.  Ser. Math. Inform. 19 (2004) 73-92.
  17. A. M. Delgado, F. Marcellán. Companion linear functionals and Sobolev inner products, Meth. and   Appl. of Anal. 11 (2004) 237-266.
  18. U. Fidalgo, J. Illán, G. López Lagomasino. Hermite Padé approximation and simultaneous quadrature formulas. J. of Approx. Theory   126 (2004), 171-197.
  19. A. Gil, J. Segura, N.M. Temme. Computing Solutions of the Modified Bessel Differential Equation for Imaginary Orders and Positive Arguments. ACM Trans. Math. Softw. 30 (2004), 145-158.
  20. A. Gil, J. Segura, N.M. Temme.  Algorithm 831: Modified Bessel Functions of Imaginary Orders and Positive Argument. ACM Trans. Math. Softw. 30 (2004), 159-164
  21. A. Deaño, A. Gil, J. Segura. New inequalities from classical Sturm theorems. J. Approx. Theory 131 (2004), 208-230.
  22. G. López Lagomasino, I. Pérez, H. Pijeira. Asymptotic of extremal polynomials in the complex plane. J. of Approx. Theory 137 (2005), 226-237.
  23. I. Area, E. Godoy, F. Marcellán,  J. J. Moreno-Balcázar. Asymptotics of Sobolev orthogonal polynomials for ?-coherent pairs of  Meixner type.  J. of Comput. and Appl. Math. 178 (2005) 21-36.
  24. A. M. Delgado, F. Marcellán, On an extension of symmetric coherent pairs of orthogonal polynomials, J. of Comput. and Appl. Math.  178 (2005) 155-168.
  25. J.S. Geronimo, D.S. Lubinsky, F. Marcellán. Asymptotics for Sobolev Orthogonal Polynomials for Exponential Weights, Constr. Approx. 22 (2005) 309-346.
  26. M. Isabel Bueno, F. Marcellán, J. Sánchez Ruiz. Continuous symmetrized Sobolev inner products of order N (I), J. Math. Anal. and Appl.  306 (2005) 83-96.
  27. J. Arvesu, A. Garrido, F. Marcellán. An electrostatic interpretation of the zeros of the Freud type orthogonal polynomials,  Electr. Trans. in Num. Anal. 19 (2005) 37-47.
  28. J. Hernández , F. Marcellán, Christoffel transforms and Hermitian linear functionals, Med. J. of Math. 2 (2005) 451-458.
  29. José M. Rodríguez, Dmitry V. Yakubovich. A Kolmogorov-Szego-Krein type condition for weighted Sobolev spaces. Indiana University Mathematical Journal 54 (2005), 575-598.
  30. V.I. Kolyada. Inequalities of Gagliardop-Niremberg type and estimates for the moduli of continuity. Russian Math. Surveys 60 (2005), 1147-1164.
  31. B. de la Calle. Error bounds for rational quadrature formulas of analytic functions.  Numerische Mathematik 101 (2005), 251-271.
  32. I. Alvarez Rocha, L. Salto. "Asymptotics of polynomials orthogonal with respect to a discrete-complex Sobolev inner product", J. Comp. and Appl. Math. 178 (2005), 1-19.
  33. J. I. de Vicente, J. Sánchez Ruiz. Separability conditions from the Landau-Pollak uncertainty relation. Physical Review A  71, 052325 (2005)
  34. J. Sánchez Ruiz, J. S. Dehesa. Fisher information of orthogonal hypergeometric polynomials. J.  of Comput.  and Appl. Math.  182 (2005), 150-164.
  35. J. Arvesú. Quantum algebras suq(2) and suq(1,1) associated with certain q-Hahn polynomials: A revisited approach. Electr. Trans. Num. Anal. 24 (2006), 24-44.
  36. M. I. Bueno, F. Marcellán. Polynomials perturbations of bilinear functionals and Hessenberg matrices. L. Alg. and Appl. 414 (2006), 64-83.
  37. A. M. Delgado, J. S. Geronimo, P. Iliev , F. Marcellán. Two variable orthogonal polynomials and structured matrices,   SIAM J. Matrix Anal. and Appl.  28 (2006) 118-147.
  38. G. Lopez, F. Marcellán, H. Pijeira. Logarithmic Asymptotics of contracted Sobolev extremal polynomials, J. Approx. Theory  143 2006), 62-73.
  39. M. Isabel Bueno, F. Marcellán, J. Sánchez Ruiz. Continuous symmetrized Sobolev inner products of order N (II), Electr. Trans. in Num. Anal.  24 (2006) 55-65.
  40. F. Marcellán, S. M. Zagorodnyuk. On the basic set of solutions of a high order linear difference equation. J. of Diff. Eq. and Appl. 12 (2006) 213-228.
  41. A. I. Aptekarev, A. Cachafeiro, F. Marcellán. A scalar Riemann boundary value problem approach to the orthogonal polynomials on the circle, J. Approx. Theory 141 (2006) 174-181.
  42. V.I. Kolyada, Mixed norms and Sobolev type inequalities. Banach Center Publ. (2006),  v. 72, 141-160.
  43. J. Hernández, F. Marcellán. Classical orthogonal polynomials and Leverrier-Faddev algorithm for the matrix pencils sE – A,  Intern. J. of  Math. and Math. Sci. (2006). Article ID 74507.
  44. José M. Rodríguez, Venancio Alvarez, Elena Romera, Domingo Pestana. Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey. Electronic Transactions in Numerical Analysis 24 (2006), 88-93.
  45. Ana Portilla, Yamilet Quintana, José M. Rodríguez, Eva Tourís. Weierstrass' Theorem in weighted Sobolev spaces with k derivatives: announcement of results. Electronic Transactions in Numerical Analysis 24 (2006), 103-107.
  46. U. Fidalgo,  G. López Lagomasino. Rate of convergence of generalized Hermite-Padé approximants of Nikishin systems. Constructive Approximation  23 (2006), 165-196.
  47. D. Barrios, B. de la Calle, G. López Lagomasino.   Ratio and relative asymptotic of polynomials orthogonal with respect to varying Denisov-type measures.   J. of Approx. Theory 139 (2006), 223-256.
  48. A. I. Aptekarev, V. Kalyagin, G. López Lagomasino, I. A. Rocha. On the limit behavior of the recurrence coefficients for multiple orthogonal polynomials  J. of Approx. Theory  139 (2006), 346-370.
  49. A. Gil, J. Segura y N.M. Temme. The ABC of Hyper Recursion. J. Comput. Appl. Math. 190 (2006), 270-286.
  50. A. Gil, J. Segura y N.M. Temme. Computing the Real Parabolic Cylinder Functions U(a,x), V(a,x). ACM Trans. Math. Softw. 32(1) (2006), 70-101.
  51. A. Gil, J. Segura y N.M. Temme. Algorithm 850:Real Parabolic Cylinder Functions U(a,x), V(a,x). ACM Trans. Math. Softw. 32(1) (2006), 102-112.
  52. R. Álvarez-Nodarse, Y. F. Smirnov, R. S. Costas-Santos. A q-analog of the Racah polynomials and q-algebra SUq(2) in quantum optics.  J. of Russian Laser Research, 27 (2006), 1-32.
  53. R. Álvarez-Nodarse, R.S. Costas-Santos. Limit relations between q-Krall type orthogonal polynomials. J. Math. Anal. Appl. 322 (2006), 158–176.
  54. J. L. Fernández, M. V. Melián, D. Pestana. Quantitative mixing results and inner functions. Math. Annalen 337 (2007), 233-251.
  55. F. Marcellán, Non standard orthogonal polynomials. Applications in Numerical Analysis and Approximation Theory, Rev. de la Acad. Col. de Cien. Exactas, Fís. y Nat. 29 (118) (2007).
  56. M. Bello, G. López Lagomasino, J. Míngues. Fourier-Padé approximation for Angelesco systems. Constructive Approximation (on-line, diciembre, 2006)
  57. A. Cachafeiro, F. Marcellán, C. Pérez, Orthogonal Polynomials with respect to the sum of an arbitrary measure and a Bernstein Szegö measure, Adv. in Comput. Math. (on-line, agosto 2006).
  58. L. Daruis, J. Hernandez, F. Marcellán, Spectral Transforms for Hermitian Toeplitz matrices, J. of  Comput. and Appl. Math. En prensa.
  59. F. Marcellán, R. Sfaxi, Second structure relation for semiclassical orthogonal polynomials, J. of  Comput. and Appl. Math. En prensa.
  60. F. Marcellán, A. Martínez Finkelshtein, P. Martínez González, Electrostatic models for zeros of polynomials: old, new, and some open problems,  J. of Comput. and Appl. Math. En prensa.
  61. R.S. Costas, F. Marcellán, Second structure relation for q-semiclassical polynomials of the Hahn Tableau, J. Math. Anal. and Appl. En prensa.
  62. F. Marcellán, J. J. Moreno-Balcazar, Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports., Acta Appl. Math. En prensa.
  63. Maria I. Bueno Cachadina, Froilan M. Dopico, A more accurate algorithm for computing the Christoffel transformation, J. of Comp. and Appl. Math. En prensa .

 

Last Updated on Monday, 15 February 2010 19:30